B$\mathrm{.}5$ This problem studies underflow and overflow in Python in more detail.

$($a$)$ Modify the code in section $2\mathrm{.}3\mathrm{.}2$ to investigate underflow for floating$-$point num$-$

bers in Python. In order to make your output manageable, make sure you start

from a number that is sufficiently small.

$($b$)$ Now investigate whether or not overflow occurs for integers in Python. Do your$-$

self a favor and start not from $1,$ but from a very large positive number and

increment from there. You should use sys$.$maxsize to get the ballpark of near

where you should start checking things. You should use type$()$ to see if the type

changes below sys$.$maxsize and above it$.$